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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
Let Y1, Y2, . . . , Yn be a random sample from a population with density function

In Exercise 9.53, you showed that Y(1) = min(Y1, Y2, . . . , Yn) is sufficient for θ.
a Find the MLE for θ.
b Find a function of the MLE in part (a) that is a pivotal quantity.
c Use the pivotal quantity from part (b) to find a 100(1 − α)% confidence interval for θ.
Exercise 9.53
Let Y1, Y2, . . . , Yn be a random sample from a population with density function

Show that Y(1) = min(Y1, Y2, . . . , Yn) is sufficient for θ.
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